Théon of Smyrna is a Platonic schoolmaster which would have lived under the reign of the emperor Hadrian, at the 2nd century, but, actually, the time to which he lived is discussed and it is difficult to date it according to what one preserved of his works.

One allots a to him Exposition of mathematical knowledge useful for the reading of Plato (in Latin: Expositio rerum mathematicarum utilium AD Platonem legendum ), written in Greek, whose only fragments are currently known thanks to two preserved manuscripts, one, the manuscript has, in Biblioteca Marciana of Venice, the other, the manuscript B, at the National library of Paris. The texts which contain these two manuscripts are different one from the other; they are, moreover, fragmentary and contain gaps even inside the preserved parts.

The manuscript has is presented in the form of a treaty of arithmetic and “music” of inspiration pythagorician; Joelle Delattre, in the thesis that it devoted to him in 1999, distinguishes two different treaties there, one, of arithmetic, the other, of music, but these two disciplines merge from the point of view Neo-Pythagorean and it could be a question of a continuous unit. The manuscript B is a course of astronomy which states to rest, lengthily (page 120 to page 198, in the Hiller edition), on writings of Adraste, now lost, then, more briefly, on Dercyllide (since page 198 until the end of the preserved text, on page 206, where the author announces a talk drawn from Thrasylle, exposed which is not preserved in the manuscript of Paris which is the only source exploited to date). The developments which rest on Adraste, although disparate, contain demonstrations of the annual movement of the Sun which testify to a scientific high level of development, in particular the demonstration of the equivalence of the assumption of the eccentric and that of the épicycle (Hiller, p. 166, L. 14 to p. 169, L. 8).

The manuscript starts with a demonstration of the rotundity of the Earth, which is based on the calculation of the volume of this one (Hiller, p. 126, L. 5-8), calculation of which the explanation (p. 126, L. 8 to p. 127, L. 6) utilized the writing archimédienne numbers by myriads, known by Arénaire of Archimedes; this calculation rests on the idea that the volume of a sphere of ray R is equal to the two-thirds of the volume of a cylinder of ray R and 2R height, idea shown by Archimedes in the Traité Sphere and Cylinder , Livre I, Proposition 34; the figures being unobtrusive in the manuscript, the editor is based on a restitution of Martin who contains an error (the volume of the ground is of 270.025.043.508.297, 3 cubic stages, and not of 269.941.043.317.821, 3, as gives Hiller; the error results from what Martin wrote 6.427.153.124 square stages, like value from (2R) 2, instead of the correct value of 6.429.153.124, and it was raised by Tannery and Dupuis). The author still shows this rotundity while being based on the shade of the Earth on the Moon at the time of a Moon eclipse and on the progressive disappearance of the objects at the horizon.

The manuscript of Paris was published by Martin (Th. - H.), Paris, 1849, accompanied by a Latin translation; a critical edition of the whole of the preserved fragments, based on the manuscripts of Venice and Paris, was given by Hiller, Leipzig (Teubner), 1878; an edition accompanied by a French translation was given by J. Dupuis, Paris, 1892. This work would not know, however, being held for final, because there would exist, in addition to the two manuscripts of Venice and Paris, two other manuscripts preserved at the Library ambrosienne of Milan. The most important source of the astronomical part of work of Théon, Adraste, is known, in addition, thanks to the important loans which the Latin Comment of Chalcidius makes him on the Timée, whose influence was considerable in the medieval Latin Occident.

Ptolémée refers to Théon of Smyrna for planet observations (Mercury, Venus), towards 130 after J. - C.